@article{oai:niigata-u.repo.nii.ac.jp:00001939,
 author = {Tamura, Hiroshi and Sengoku, Masakazu and Shinoda, Shoji and Abe, Takeo},
 issue = {10},
 journal = {IEICE transactions on fundamentals of electronics, communications and computer sciences, IEICE transactions on fundamentals of electronics, communications and computer sciences},
 month = {Oct},
 note = {In a cellular mobile system, assigning a channel for a call in a cell so as to achieve high spectral efficiency is an important problem. In usual channel assignment for a cellular mobile system, a channel can be simultaneously assigned to some cells with a constant separation distance. This usual model of a cellular mobile system has been formulated using a graph and it is known that the channel assignment problem is equivalent to the coloring problem of graph theory. Recently, a new channel assignment scheme has been proposed. This scheme takes the degree of interference into consideration. In the scheme, a channel is simultaneously assigned if the CIR (carrier-to-interference ratio) is more than the desired value. In this paper, we formulate this new model using a network and a new coloring problem of networks. The new coloring problem of networks is a generalization of the usual coloring problem of graphs. One of the merits of this formulation is that the degree of cochannel interference between cells can be represented. In the usual formulation using a graph, the degree of cochannel interference between cells can not be represented. Therefore, spectral efficiency in the formulation using a network is higher than spectral efficiency in the formulation using a graph. In this paper, we show that the new coloring problem is an NP-hard problem. Subsequently, we rewrite the new coloring problem of networks to a coloring problem of graphs on some assumptions and consider the relation between the results on the new coloring and the results on the usual coloring.},
 pages = {2983--2989},
 title = {Channel Assignment Problem in a Cellular Mobile System and a New Coloring Problem of Networks},
 volume = {E74-A},
 year = {1991}
}